Variational formulation of problems involving fractional order differential operators

In this work, we consider boundary value problems involving either Caputo or Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to nonsymmetric boundary value problems, which are investigated from a variational point of view. The variational problem for the Riemann-Liouville case is coercive on the space Hα/2 0 (0, 1) but the solutions are less regular, whereas that for the Caputo case involves different test and trial spaces. The numerical analysis of these problems requires the so-called shift theorems which show that the solutions of the variational problem are more regular. The regularity pickup enables one to establish convergence rates of the finite element approximations. The analytical theory is then applied to the Sturm-Liouville problem involving a fractional derivative in the leading term. Finally, extensive numerical results are presented to illustrate the error estimates for the source problem and eigenvalue problem

Vulnerable warriors: the atmospheric marketing of military and policing equipment before and after 9/11

In this article, we analyse changes in the circulation of advertisements of policing products at security expos between 1995 and 2013. While the initial aim of the research was to evidence shifts in terrorist frames in the marketing of policing equipment before and after 9/11, our findings instead suggested that what we are seeing is the rise of marketing to police as “vulnerable warriors”, law enforcement officers in need of military weapons both for their offensive capabilities and for the protection they can offer to a police force that is always under threat

Coupling Of Two Dimensional Viscous And Inviscid Incompressible Stokes Equations

INTRODUCTION A domain decomposition approach usually consists in the decomposition of the possibly complex domain into subdomains of simpler shape. Then the original problem is reduced to a sequence of subproblems for the same partial differential equation which can be solved independently to some extent [7, 10, 11, 14, 16]. Another very interesting area for the application of domain decomposition procedures is the coupling of partial differential equations of different type each used in a suitable subregion of the whole domain. A typical situation is the investigation of an incompressible flow around an obstacle. All the interesting features of the flow occur near the boundary of the obstacle due to the important role of viscosity effects in this area. In the region far away from the obstacle one can neglect viscosity effects. For numerical and theoretical reasons it would be interesting to combine the solution to the Navier-Stokes equations in an inner subregion near the boundary o